Gas Dynamics-Nozzles and Diffusers

ConCon--Div DiffuserDiv Diffuser

ØØ With most present day aircraft engines, it is With most present day aircraft engines, it is necessary to decelerate the air to subsonic necessary to decelerate the air to subsonic velocity before passing it to the engine, this velocity before passing it to the engine, this deceleration also increases the pressure of the deceleration also increases the pressure of the incoming air. The deceleration is carried out in incoming air. The deceleration is carried out in the diffuser.the diffuser.

ØØ The deceleration potentially being shockThe deceleration potentially being shock--less at less at the design flight Mach number of the aircraft.the design flight Mach number of the aircraft.

In such a case the flow through the In such a case the flow through the diffuser will be as shown in the following figure.diffuser will be as shown in the following figure.

PDF created with pdfFactory trial version www.pdffactory.com

http://www.pdffactory.com


Diffuser with different Inlet Mach numberDiffuser with different Inlet Mach number

M < MM < Mdesdes




Cont..Cont..

M > MM > Mdesdes

nn Increase in Mach number will cause the Shock Increase in Mach number will cause the Shock wave to be “swallowed” by the diffuser and the wave to be “swallowed” by the diffuser and the shock wave then settles in the divergent portion shock wave then settles in the divergent portion of the diffuser as shown in the above figure.of the diffuser as shown in the above figure.




Cont..Cont..




Diffuser PerformanceDiffuser Performance




Stagnation pressure ratio versus Mach numberStagnation pressure ratio versus Mach number

P P –– Static Pr .Static Pr .PPt t -- Total Pr .Total Pr .

nn Total Pr . Ratio is least sensitive to variations of Total Pr . Ratio is least sensitive to variations of γγ




Cont..Cont..

T T –– Static Temp.Static Temp.TTt t -- Total Temp.Total Temp.

T/ TT/ Ttt ratio relatively insensitive to variations in ratio relatively insensitive to variations in γγ below below M M ≈≈ 0.80.8




Cont..Cont..Area ratio versus Mach numberArea ratio versus Mach number

Area ratio relatively insensitive to variations in Area ratio relatively insensitive to variations in γγ below below M ≈ 1.5 M ≈ 1.5




Limitations of Gas tablesLimitations of Gas tables

1.1. They do not show trends or the ‘big They do not show trends or the ‘big picture. ’picture. ’

2.2. There is almost always the need for There is almost always the need for interpolation.interpolation.

3.3. They display only one or at most a few They display only one or at most a few values of values of γγ..

4.4. They do not necessarily have the They do not necessarily have the required accuracy.required accuracy.




Question 1Question 1How to locate sonic state on the THow to locate sonic state on the T--s diagram?s diagram?

If the flow is subsonic, the sonic state will be below its If the flow is subsonic, the sonic state will be below its static state.static state.If the flow is supersonic, the sonic state will be above its If the flow is supersonic, the sonic state will be above its static state.static state.




Question 2Question 2A large supply chamber containing air at 6.0 atm and A large supply chamber containing air at 6.0 atm and 300K is connected to a converging nozzle on the left 300K is connected to a converging nozzle on the left side and a Cside and a C--D nozzle on the right side. Both nozzles D nozzle on the right side. Both nozzles share the same minimum passage area of 100 sq.cm. share the same minimum passage area of 100 sq.cm. The CThe C--D nozzle has an exitD nozzle has an exit--toto--throat area ratio of 1.2throat area ratio of 1.2

PPambamb

a) Let us consider the converging nozzle at the left anda) Let us consider the converging nozzle at the left andcompare the pressure level at point A, C, and D.compare the pressure level at point A, C, and D.




Cont..Cont..




Cont..Cont..

b) b) IfIf the ambient pressurethe ambient pressure is reduced to 5.0 atm. What is the is reduced to 5.0 atm. What is the mass flow rate in the nozzle?mass flow rate in the nozzle?




Cont..Cont..

From the Temperature ratio From the Temperature ratio TTexit exit isisTTexitexit = 284.8 K= 284.8 K




Cont..Cont..How much do we need to lower the ambient pressure to reach the choking point of this converging nozzle?For a converging nozzle, the ambient pressure has to be For a converging nozzle, the ambient pressure has to be lower than 52.8% of the chamber pressure to choke the lower than 52.8% of the chamber pressure to choke the converging nozzle. This corresponds to an ambient converging nozzle. This corresponds to an ambient pressure ofpressure of

PPambamb ≤ 3.17 atm ≤ 3.17 atm

If PIf Pambamb is lower than 3.17 atm, the exit plane pressure is lower than 3.17 atm, the exit plane pressure will not be the same as the ambient value (pressure will not be the same as the ambient value (pressure mismatch). Pmismatch). Pambamb will keep staying at 3.17 atm. This is will keep staying at 3.17 atm. This is because no downstream pressure information canbecause no downstream pressure information canpropagate upstream past the sonic point (exit plane). propagate upstream past the sonic point (exit plane). The flow within the nozzle becomes invariant once the The flow within the nozzle becomes invariant once the sonic condition is attained at the exit.sonic condition is attained at the exit.




What is the mass flow rate at choking condition?What is the mass flow rate at choking condition?

For a con. nozzle the ambient pressure has to be lower than 52.8% of For a con. nozzle the ambient pressure has to be lower than 52.8% of the chamber pressure to choke the con. Nozzle. This corresponds to the chamber pressure to choke the con. Nozzle. This corresponds to an amb. Pr . of Pan amb. Pr . of Pamb amb ≤ ≤ 3.17 atm.3.17 atm.

When When PPamb amb = = 3.17 atm, the Mach no. at the exit plane just reaches 3.17 atm, the Mach no. at the exit plane just reaches unity. From Isentropiv table at M = 1 unity. From Isentropiv table at M = 1




Let us consider CLet us consider C--D nozzle on the rightD nozzle on the rightIf the ambient pressure is set at 5.0 atm, do you expect the mass flow rate in the C-D nozzle to be the same as that in the converging nozzle computed before?

n For this C-D nozzle case, we also need to check if the nozzle is choked at Pamb = 5.0 atm. The main difference between the C-D nozzle and the converging nozzle is that the choking pressure ratio is dependent on the exit-to-throat area ratio (not a universal constant anymore).

n With an area ratio of 1.20, we find from the isentropic flow table that the subsonic solution gives a pressure ratio

n Hence, we conclude that- the ambient pressure is high enough that the flow is

not choked- the flow remains subsonic within the C-D nozzle- ρexit, Mexit and Texit are the same as those in the converging nozzle

case




Cont..Cont..Since the exit area is 1.20 times as large as that of the Since the exit area is 1.20 times as large as that of the converging nozzle, we expect a 20 % increase in the converging nozzle, we expect a 20 % increase in the mass flow rate. Hence, m.f.r is 12.96 kg/mmass flow rate. Hence, m.f.r is 12.96 kg/m3. 3.

How much do we need to lower the ambient pressure for the nozzle to operate at its first critical point?The first critical point corresponds to an isentropic, subsonic solution with Mach 1.0 flow at the throat.

We obtain from the isentropic flow table that

What is the corresponding mass flow rate at the first critical point?

Once this convergingOnce this converging--diverging nozzle is choked at its first critical diverging nozzle is choked at its first critical point, we know that Mach 1.0 is achieved at its minimum flow area, point, we know that Mach 1.0 is achieved at its minimum flow area, i.e. at the throat. We expect that same m.f.r as that of the i.e. at the throat. We expect that same m.f.r as that of the converging nozzle choked case converging nozzle choked case




Cont..Cont..At the design point (third critical)At the design point (third critical)

What is the ambient pressure?The third critical point corresponds to an isentropic, supersonic The third critical point corresponds to an isentropic, supersonic solution in the Csolution in the C--D nozzle.D nozzle.

For an area ratio of 1.20, we obtain a supersonic solution from the For an area ratio of 1.20, we obtain a supersonic solution from the isentropic flow table Misentropic flow table Mexitexit = 1.534= 1.534

This solution gives a pressure ratio PThis solution gives a pressure ratio Pambamb/P/P00 = 0.25922, so= 0.25922, soPPambamb = 1.55 atm= 1.55 atm

Look back to our calculations:Look back to our calculations:

nn How do you compare the ambient pressure which is How do you compare the ambient pressure which is required to choke the converging and Crequired to choke the converging and C--D nozzle? Which D nozzle? Which one is higher? Can you explain it?one is higher? Can you explain it?




Cont..Cont..




Cont..Cont..




Isentropic Nozzle flowIsentropic Nozzle flow




11--DD Flow through constant area ductsFlow through constant area ducts

a)a) Adiabatic duct flow with FrictionAdiabatic duct flow with Friction( ( FannoFanno Flow)Flow)

b) Duct flow with Heat Transfer and b) Duct flow with Heat Transfer and negligible friction ( negligible friction ( RayleighRayleigh Flow)Flow)




Documents

Gas Dynamics-Nozzles and Diffusers